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Necessary and sufficient criteria for existence, regularity, and asymptotic stability of enhanced pullback attractors with applications to 3D primitive equations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230802
Renhai Wang, Boling Guo, Daiwen HuangWe introduce several new concepts called enhanced pullback attractors for nonautonomous dynamical systems by improving the compactness and attraction of the usual pullback attractors in strong topology spaces uniformly over some infinite time intervals. Then we establish several necessary and sufficient criteria for the existence, regularity and asymptotic stability of these enhanced pullback attractors

A IETIDP method for discontinuous Galerkin discretizations in isogeometric analysis with inexact local solvers Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230802
Monica Montardini, Giancarlo Sangalli, Rainer Schneckenleitner, Stefan Takacs, Mattia TaniWe construct solvers for an isogeometric multipatch discretization, where the patches are coupled via a discontinuous Galerkin approach, which allows for the consideration of discretizations that do not match on the interfaces. We solve the resulting linear system using a DualPrimal IsogEometric Tearing and Interconnecting (IETIDP) method. We are interested in solving the arising patchlocal problems

Conforming and nonconforming virtual element methods for fourth order nonlocal reaction diffusion equation Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230724
Dibyendu Adak, Verónica Anaya, Mostafa Bendahmane, David MoraIn this work, we have designed conforming and nonconforming virtual element methods (VEM) to approximate nonstationary nonlocal biharmonic equation on general shaped domain. By employing Faedo–Galerkin technique, we have proved the existence and uniqueness of the continuous weak formulation. Upon applying Brouwer’s fixed point theorem, the wellposedness of the fully discrete scheme is derived. Further

Asymptotic behavior of a threedimensional haptotactic crossdiffusion system modeling oncolytic virotherapy Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230722
Yifu Wang, Chi XuThis paper deals with an initialboundary value problem for a doubly haptotactic crossdiffusion system arising from the oncolytic virotherapy ut=Δu−∇⋅(u∇v)+μu(1−u)−uz,vt=−(u+w)v,wt=Δw−∇⋅(w∇v)−w+uz,zt=DzΔz−z−uz+βw, in a smoothly bounded domain Ω⊂ℝ3 with β>0, μ>0 and Dz>0. Based on a selfmap argument, it is shown that under the assumption βmax{1,∥u0∥L∞(Ω)}<1+(1+1minx∈Ωu0(x))−1, this problem possesses

Regular solutions of chemotaxisconsumption systems involving tensorvalued sensitivities and Robin type boundary conditions Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230722
Jaewook Ahn, Kyungkeun Kang, Jihoon LeeThis paper deals with a parabolic–elliptic chemotaxisconsumption system with tensorvalued sensitivity S(x,n,c) under noflux boundary conditions for n and Robintype boundary conditions for c. The global existence of bounded classical solutions is established in dimension two under general assumptions on tensorvalued sensitivity S. One of the main steps is to show that ∇c(⋅,t) becomes tiny in L2(Br(x)∩Ω)

Global classical solvability and stabilization in a twodimensional chemotaxis–fluid system with sublogarithmic sensitivity Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230720
Ji LiuIn this paper, we consider the following system: nt+u⋅∇n=Δn−∇⋅(nχ(c)∇c),ct+u⋅∇c=Δc−cn,ut+κ(u⋅∇)u=Δu+∇P+n∇Φ, in a smoothly bounded domain Ω⊂ℝ2, with κ∈{0,1} and a given function χ(c)=1c𝜃 with 𝜃∈[0,1). It is proved that if κ=1 then for appropriately small initial data an associated noflux/noflux/Dirichlet initialboundary value problem is globally solvable in the classical sense, and that if κ=0

Analysis of complex chemotaxis models Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230714
Youshan Tao, Michael WinklerThis preface describes motivational aspects related to a special issue focusing on “analysis of complex chemotaxis models”, and briefly discusses the contributions provided by the six papers contained therein.

Existence of multispikes in the Keller–Segel model with logistic growth Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230714
Fanze Kong, Juncheng Wei, Liangshun XuThe Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of unicellular and multicellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex nontrivial patterns. This paper is devoted to the construction of multispiky solutions to the

Critical mass for Keller–Segel systems with supercritical nonlinear sensitivity Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230714
Xuan Mao, Yuxiang LiThis paper is concerned with the following radially symmetric Keller–Segel systems with nonlinear sensitivity ut=Δu−∇⋅(u(1+u)α−1∇v) and 0=Δv−⨍Ωudx+u, posed on Ω={x∈ℝn:x2n. Here we consider the supercritical case α≥2n and show a critical mass phenomenon. Precisely, we prove that there exists a critical mass mc:=mc(n,R,α) such that (1) for arbitrary nonincreasing nonnegative initial data u0(x)=u0(x)

Compressible Euler–Maxwell limit for global smooth solutions to the Vlasov–Maxwell–Boltzmann system Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230706
Renjun Duan, Dongcheng Yang, Hongjun YuTwo fundamental models in plasma physics are given by the Vlasov–Maxwell–Boltzmann system and the compressible Euler–Maxwell system which both capture the complex dynamics of plasmas under the selfconsistent electromagnetic interactions at the kinetic and fluid levels, respectively. It has remained a longstanding open problem to rigorously justify the hydrodynamic limit from the former to the latter

Global boundedness in a 2D chemotaxisNavier–Stokes system with flux limitation and nonlinear production Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230706
Wei WangWe consider the chemotaxisNavier–Stokes system with gradientdependent flux limitation and nonlinear production: nt+u⋅∇n=Δn−∇⋅(nf(∇c2)∇c), ct+u⋅∇c=Δc−c+g(n), ut+(u⋅∇)u+∇P=Δu+n∇ϕ and ∇⋅u=0 in a bounded domain Ω⊂ℝ2, where the flux limitation function f∈C2([0,∞]) and the signal production function g∈C1([0,∞]) generalize the prototypes f(s)=Kf(1+s)−α2 and g(s)=Kgs(1+s)β−1 with Kf,Kg>0, α∈ℝ and β>0.

Threespecies driftdiffusion models for memristors Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230629
Clément Jourdana, Ansgar Jüngel, Nicola ZamponiA system of driftdiffusion equations for the electron, hole, and oxygen vacancy densities in a semiconductor, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet–Neumann boundary conditions. This system describes the dynamics of charge carriers in a memristor device. Memristors can be seen as nonlinear resistors with memory, mimicking the

An effective model for boundary vortices in thinfilm micromagnetics Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230621
Radu Ignat, Matthias KurzkeFerromagnetic materials are governed by a variational principle which is nonlocal, nonconvex and multiscale. The main object is given by a unitlength threedimensional vector field, the magnetization, that corresponds to the stable states of the micromagnetic energy. Our aim is to analyze a thin film regime that captures the asymptotic behavior of boundary vortices generated by the magnetization and

Human behavioral crowds review, critical analysis and research perspectives Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230606
Nicola Bellomo, Jie Liao, Annalisa Quaini, Lucia Russo, Constantinos SiettosThis paper presents a survey and critical analysis of the mathematical literature on modeling and simulation of human crowds taking into account behavioral dynamics. The main focus is on research papers published after the review [N. Bellomo and C. Dogbè, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives, SIAM Rev. 53 (2011) 409–463], thus providing important

Crossdiffusion models in complex frameworks from microscopic to macroscopic Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230606
D. Burini, N. ChouhadThis paper deals with the micro–macro derivation of models from the underlying description provided by methods of the kinetic theory for active particles. We consider the socalled exotic models according to the definition proposed in [ N. Bellomo, N. Outada, J. Soler, Y. Tao and M. Winkler, Chemotaxis and cross diffusion models in complex environments: Modeling towards a multiscale vision, Math. Models

Adaptive isogeometric methods with C1 (truncated) hierarchical splines on planar multipatch domains Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230531
Cesare Bracco, Carlotta Giannelli, Mario Kapl, Rafael VázquezIsogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensorproduct structure of standard multivariate Bspline models is not well suited for the representation of complex geometries, and to maintain high continuity on general domains special constructions on multipatch geometries

Singular patterns in Keller–Segeltype models Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230529
Juan Campos, Carlos Pulido, Juan Soler, Mario VerueteThe aim of this paper is to elucidate the existence of patterns for Keller–Segeltype models that are solutions of the traveling pulse form. The idea is to search for transport mechanisms that describe this type of waves with compact support, which we find in the socalled nonlinear diffusion through saturated flux mechanisms for the movement cell. At the same time, we analyze various transport operators

Multigrid solvers for isogeometric discretizations of the second biharmonic problem Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230529
Jarle Sogn, Stefan TakacsWe develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zeroorder term. In a previous paper, the authors have developed an analysis for the first biharmonic problem based on Hackbusch’s framework. This analysis can only be extended to the second biharmonic problem if one assumes uniform grids. In this paper, we prove a multigrid

Nonisothermal nonNewtonian fluids: The stationary case Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230525
Maurizio Grasselli, Nicola Parolini, Andrea Poiatti, Marco VeraniThe stationary Navier–Stokes equations for a nonNewtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlettype boundary conditions. The viscosity is supposed to depend on the temperature and the stress depends on the strain through a suitable power law depending on p∈(1,2) (shear thinning case). For this problem we establish the existence of a weak solution

Numerical modeling of the brain poromechanics by highorder discontinuous Galerkin methods Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230520
Mattia Corti, Paola F. Antonietti, Luca Dede’, Alfio M. QuarteroniWe introduce and analyze a discontinuous Galerkin method for the numerical modeling of the equations of MultipleNetwork Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids. Concerning the spatial discretization, we employ a highorder discontinuous Galerkin method on polygonal and polyhedral

Boundedness and large time behavior of solutions of a higherdimensional haptotactic system modeling oncolytic virotherapy Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230520
Jiashan Zheng, Yuanyuan KeThis paper is concerned with the higherdimensional haptotactic system modeling oncolytic virotherapy, which was initially proposed by Alzahrani–Eftimie–Trucu [Multiscale modelling of cancer response to oncolytic viral therapy, Math. Biosci. 310 (2019) 76–95] (see also the survey Bellomo–Outada et al. [Chemotaxis and crossdiffusion models in complex environments: Models and analytic problems toward

Analysis of a fullydiscrete, nonconforming approximation of evolution equations and applications Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230517
A. Kaltenbach, M. RůžičkaIn this paper, we consider a fullydiscrete approximation of an abstract evolution equation deploying a nonconforming spatial approximation and finite differences in time (Rothe–Galerkin method). The main result is the convergence of the discrete solutions to a weak solution of the continuous problem. Therefore, the result can be interpreted either as a justification of the numerical method or as

Lack of robustness and accuracy of many numerical schemes for phasefield simulations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230516
Jinchao Xu, Xiaofeng XuIn this paper, we study the stability, accuracy and convergence behavior of various numerical schemes for phasefield modeling through a simple ODE model. Both theoretical analysis and numerical experiments are carried out on this ODE model to demonstrate the limitation of most numerical schemes that have been used in practice. One main conclusion is that the firstorder fully implicit scheme is the

Variational multiscale method stabilization parameter calculated from the strainrate tensor Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230515
Kenji Takizawa, Yuto Otoguro, Tayfun E. TezduyarThe stabilization parameters of the methods like the StreamlineUpwind/Petrov–Galerkin, PressureStabilizing/Petrov–Galerkin, and the Variational Multiscale method typically involve two local length scales. They are the advection and diffusion length scales, appearing in the expressions for the advective and diffusive limits of the stabilization parameter. The advection length scale has always been

L1Theory for HeleShaw flow with linear drift Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230511
Noureddine IgbidaThe main goal of this paper is to prove L1comparison and contraction principles for weak solutions of PDE system corresponding to a phase transition diffusion model of HeleShaw type with addition of a linear drift. The flow is considered with a source term and subject to mixed homogeneous boundary conditions: Dirichlet and Neumann. The PDE can be focused to model for instance biological applications

The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230510
Patrick HenningIn this paper, we consider the generalized inverse iteration for computing ground states of the Gross–Pitaevskii eigenvector (GPE) problem. For that we prove explicit linear convergence rates that depend on the maximum eigenvalue in magnitude of a weighted linear eigenvalue problem. Furthermore, we show that this eigenvalue can be bounded by the first spectral gap of a linearized Gross–Pitaevskii operator

A nonlinear bending theory for nematic LCE plates Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230504
Sören Bartels, Max Griehl, Stefan Neukamm, David PadillaGarza, Christian PalusIn this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stressfree in the flat reference configuration, the top layer features an eigenstrain that depends on the local liquid crystal orientation. As a consequence, the plate shows nonflat deformations

Collective behaviors of stochastic agentbased models and applications to finance and optimization Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230426
Dongnam Ko, SeungYeal Ha, Euntaek Lee, Woojoo ShimIn this paper, we present a survey of recent progress on the emergent behaviors of stochastic particle models which arise from the modeling of collective dynamics. Collective dynamics of interacting autonomous agents is ubiquitous in nature, and it can be understood as a formation of concentration in a state space. The jargons such as aggregation, herding, flocking and synchronization describe such

Generalized solution and eventual smoothness in a logarithmic Keller–Segel system for criminal activities Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230408
Bin Li, Li XieThis paper focuses on a simplified variant of the Short et al. model, which is originally introduced by Rodríguez, and consists of a system of two coupled reaction–diffusionlike equations — one of which models the spatiotemporal evolution of the density of criminals and the other of which describes the dynamics of the attractiveness field. Such model is apparently comparable to the logarithmic Keller–Segel

Analysis of divergence free conforming virtual elements for the Brinkman problem Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230407
Xuehai Huang, Feng WangIn this paper, we develop stability analysis, including inverse inequality, L2 norm equivalence and interpolation error estimates, for divergence free conforming virtual elements in arbitrary dimension. A local energy projector based on the local Stokes problem is suggested, which commutes with the divergence operator. After defining a discrete bilinear form and a stabilization involving only the boundary

Traveling waves for a Fishertype reaction–diffusion equation with a flux in divergence form Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230407
Margarita Arias, Juan CamposAnalysis of the speed of propagation in parabolic operators is frequently carried out considering the minimal speed at which its traveling waves (TWs) move. This value depends on the solution concept being considered. We analyze an extensive class of Fishertype reaction–diffusion equations with flows in divergence form. We work with regular flows, which may not meet the standard elliptical conditions

Mathematical modeling of glioma invasion and therapy approaches via kinetic theory of active particles Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230331
Martina Conte, Yvonne Dzierma, Sven Knobe, Christina SurulescuA multiscale model for glioma spread in brain tissue under the influence of vascularization and vascular endothelial growth factors is proposed. It accounts for the interplay between the different components of the neoplasm and the healthy tissue and it investigates and compares various therapy approaches. Precisely, these involve radiotherapy and chemotherapy in a concurrent or adjuvant manner together

Multilevel domain uncertainty quantification in computational electromagnetics Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230330
Rubén Aylwin, Carlos JerezHanckes, Christoph Schwab 2 , ‡, Jakob ZechWe continue our study [R. Aylwin, C. JerezHanckes, C. Schwab and J. Zech, Domain uncertainty quantification in computational electromagnetics, SIAM/ASA J. Uncertain. Quant.8 (2020) 301–341] of the numerical approximation of timeharmonic electromagnetic fields for the Maxwell lossy cavity problem for uncertain geometries. We adopt the same affineparametric shape parametrization framework, mapping

A mean field game model of firmlevel innovation Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230329
Matt Barker, Pierre Degond, Ralf Martin, Mirabelle MuûlsKnowledge spillovers occur when a firm researches a new technology and that technology is adapted or adopted by another firm, resulting in a social value of the technology that is larger than the initially predicted private value. As a result, firms systematically underinvest in research compared with the socially optimal investment strategy. Understanding the level of underinvestment, as well as

Convergence of a particle method for a regularized spatially homogeneous Landau equation Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230328
José A. Carrillo, Matias G. Delgadino, Jeremy S. H. WuWe study a regularized version of the Landau equation, which was recently introduced in [J. A. Carrillo, J. Hu, L. Wang and J. Wu, A particle method for the homogeneous Landau equation, J. Comput. Phys. X7 (2020) 100066, 24] to numerically approximate the Landau equation with good accuracy at reasonable computational cost. We develop the existence and uniqueness theory for weak solutions, and we reinforce

Dual naturalnorm a posteriori error estimators for reduced basis approximations to parametrized linear equations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230328
P. Edel, Y. MadayIn this work, the concept of dual naturalnorm for parametrized linear equations is used to derive residualbased a posteriori error bounds characterized by a 𝒪(1) stability constant. We translate these error bounds into very effective practical a posteriori error estimators for reduced basis approximations and show how they can be efficiently computed following an offline/ online strategy. We prove

Taylor–Couette flow with temperature fluctuations: Time periodic solutions Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230325
Eduard Feireisl, YoungSam KwonWe consider the motion of a viscous compressible and heat conducting fluid confined in the gap between two rotating cylinders (Taylor–Couette flow). The temperature of the cylinders is fixed but not necessarily constant. We show that the problem admits a timeperiodic solution as soon as the ratio of the angular velocities of the two cylinders is a rational number.

Fast and slow clustering dynamics of Cucker–Smale ensemble with internal oscillatory phases Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230321
SeungYeal Ha, Jeongho Kim, Jinyeong ParkWe study fast and slow clustering dynamics of Cucker–Smale ensemble with internal phase dynamics via the Cucker–Smale–Kuramoto (in short, CSK) model. The CSK model describes the emergent dynamics of flocking particles with phase dynamics. It consists of the Cucker–Smale flocking model and the Kuramoto model, and their interplay is registered in the communication weight function between particles. We

The virtual element method for the 3D resistive magnetohydrodynamic model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230316
Lourenço Beirão da Veiga, Franco Dassi, Gianmarci Manzini, Lorenzo MascottoWe present a fourfield virtual element discretization for the timedependent resistive magnetohydrodynamics equations in three space dimensions, focusing on the semidiscrete formulation. The proposed method employs general polyhedral meshes and guarantees velocity and magnetic fields that are divergence free up to machine precision. We provide a full convergence analysis under suitable regularity

Elastic stabilization of an intrinsically unstable hyperbolic flow–structure interaction on the 3D halfspace Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230313
Abhishek Balakrishna, Irena Lasiecka, Justin T. WebsterThe strong asymptotic stabilization of 3D hyperbolic dynamics is achieved by a damped 2D elastic structure. The model is a Neumann wavetype equation with low regularity coupling conditions given in terms of a nonlinear von Karman plate. This problem is motivated by the elimination of aeroelastic instability (sustained oscillations of bridges, airfoils, etc.) in engineering applications. Empirical

Boundpreserving finite element approximations of the Keller–Segel equations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230313
Santiago Badia, Jesús Bonilla, Juan Vicente GutiérrezSantacreuThis paper aims to develop numerical approximations of the Keller–Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or cell) density, which is a positive variable, and the chemoattractant density, which is a nonnegative variable. We propose two algorithms, which combine a stabilized

Pressurerelaxation limit for a onevelocity Baer–Nunziato model to a Kapila model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230313
Cosmin Burtea, Timothée CrinBarat, Jin TanIn this paper, we study a singular limit problem for a compressible onevelocity bifluid system. More precisely, we show that solutions of the Kapila system generated by initial data close to equilibrium are obtained in the pressurerelaxation limit from solutions of the Baer–Nunziato (BN) system. The convergence rate of this process is a consequence of our stability result. Besides the fact that the

Wellposedness of a Navier–Stokes–Cahn–Hilliard system for incompressible twophase flows with surfactant Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230313
Andrea Di Primio, Maurizio Grasselli, Hao WuWe investigate a diffuseinterface model that describes the dynamics of viscous incompressible twophase flows with surfactant. The resulting system of partial differential equations consists of a sixthorder Cahn–Hilliard equation for the difference of local concentrations of the binary fluid mixture coupled with a fourthorder Cahn–Hilliard equation for the local concentration of the surfactant.

Entropy dissipation and propagation of chaos for the uniform reshuffling model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230313
Fei Cao, PierreEmmanuel Jabin, Sebastien Motsch 3 , *We investigate the uniform reshuffling model for money exchanges: two agents picked uniformly at random redistribute their dollars between them. This stochastic dynamics is of meanfield type and eventually leads to a exponential distribution of wealth. To better understand this dynamics, we investigate its limit as the number of agents goes to infinity. We prove rigorously the socalled propagation

Kinetic modeling of a leader–follower system in crowd evacuation with collective learning Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230310
Jie Liao, Yi’ang Ren, Wenbin YanA kinetic modeling of crowd evacuation with leaders and followers is considered in this paper, in which the followers may not know the full information about the walking environment and the evacuation strategy, but they follow the leaders and learn the walking strategy to get out of the walking venue. Based on the kinetic theory of active particles, the learning dynamics are considered by introducing

Modeling and numerical simulations of multilane vehicular traffic by active particles methods Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230310
M. ZagourThis paper deals with the modeling and numerical simulations of multilane vehicular traffic according to the kinetic theory of active particles methods. The main idea of this theory is to consider each driver–vehicle system as a microsystem, where the microscopic state of particles is described by position, velocity, and activity which is an appropriate variable for modeling the quality of the drivervehicle

Editorial: Active particle models and methods in science and society Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230308
N. Bellomo, F. BrezziThis editorial paper reviews the articles published in a special issue devoted to the application of active particle methods to the study of the collective dynamics of large systems of interacting entities in science and society. The applications presented in this special issue focus on the study of financial markets, cell dynamics in the context of cancer modeling, crowd vehicle and crowd dynamics

Immersed virtual element methods for electromagnetic interface problems in three dimensions Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230306
Shuhao Cao, Long Chen, Ruchi GuoFinite element methods for electromagnetic problems modeled by Maxwelltype equations are highly sensitive to the conformity of approximation spaces, and nonconforming methods may cause loss of convergence. This fact leads to an essential obstacle for almost all the interfaceunfitted mesh methods in the literature regarding the application to electromagnetic interface problems, as they are based

A diffusedomainbased numerical method for a chemotaxisfluid model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230223
Chenxi Wang, Alina Chertock, Shumo Cui, Alexander Kurganov, Zhen ZhangIn this paper, we consider a coupled chemotaxisfluid system that models selforganized collective behavior of oxytactic bacteria in a sessile drop. This model describes the biological chemotaxis phenomenon in the fluid environment and couples a convective chemotaxis system for the oxygenconsuming and oxytactic bacteria with the incompressible Navier–Stokes equations subject to a gravitational force

Time fractional gradient flows: Theory and numerics Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230223
Wenbo Li, Abner J. SalgadoWe develop the theory of fractional gradient flows: an evolution aimed at the minimization of a convex, lower semicontinuous energy, with memory effects. This memory is characterized by the fact that the negative of the (sub)gradient of the energy equals the socalled Caputo derivative of the state. We introduce the notion of energy solutions, for which we provide existence, uniqueness and certain

Control of the Stefan problem in a periodic box Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230225
Borjan Geshkovski, Debayan MaityIn this paper, we consider the onephase Stefan problem with surface tension, set in a twodimensional striplike geometry, with periodic boundary conditions respect to the horizontal direction x1∈𝕋. We prove that the system is locally nullcontrollable in any positive time, by means of a control supported within an arbitrary open and nonempty subset. We proceed by a linear test and duality, but

On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230222
Rémi Abgrall, Mária LukáčovaMedvid’ová, Philipp ÖffnerIn this work, we prove the convergence of residual distribution (RD) schemes to dissipative weak solutions of the Euler equations. We need to guarantee that the RD schemes are fulfilling the underlying structure preserving methods properties such as positivity of density and internal energy. Consequently, the RD schemes lead to a consistent and stable approximation of the Euler equations. Our result

Uniqueness and uniform structural stability of Poiseuille flows in a periodic pipe with Navier boundary conditions Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230220
Yun Wang, Chunjing XieIn this paper, we prove the uniqueness and structural stability of Poiseuille flows for axisymmetric solutions of steady Navier–Stokes system supplemented with Navier boundary conditions in a periodic pipe. Moreover, the stability is uniform with respect to both the flux and the slip coefficient of Navier boundary conditions. It is also shown that the nonzero frequency part of the velocity is bounded

A unified framework for Navier–Stokes Cahn–Hilliard models with nonmatching densities Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230216
M. F. P. ten Eikelder, K. G. van der Zee, I. Akkerman, D. SchillingerOver the last decades, many diffuseinterface Navier–Stokes Cahn–Hilliard (NSCH) models with nonmatching densities have appeared in the literature. These models claim to describe the same physical phenomena, yet they are distinct from one another. The overarching objective of this work is to bring all of these models together by laying down a unified framework of NSCH models with nonzero mass fluxes

Consensusbased optimization via jumpdiffusion stochastic differential equations Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230217
Dante Kalise, Akash Sharma, Michael V. TretyakovWe introduce a new consensusbased optimization (CBO) method where an interacting particle system is driven by jumpdiffusion stochastic differential equations (SDEs). We study wellposedness of the particle system as well as of its meanfield limit. The major contributions of this paper are proofs of convergence of the interacting particle system towards the meanfield limit and convergence of a discretized

Nonmeanfield Vicsektype models for collective behavior Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230202
Paolo Buttà, Ben Goddard, Thomas M. Hodgson, Michela Ottobre, Kevin J. PainterWe consider interacting particle dynamics with Vicsektype interactions, and their macroscopic Partial Differential Equation (PDE) limit, in the nonmeanfield regime; that is, we consider the case in which each particle/agent in the system interacts only with a prescribed subset of the particles in the system (for example, those within a certain distance). In this nonmeanfield regime the influence

On an elastic strainlimiting special Cosserat rod model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230130
K. R. Rajagopal, C. RodriguezMotivated by recent strainlimiting models for solids and biological fibers, we introduce the first intrinsic set of nonlinear constitutive relations, between the geometrically exact strains and the components of the contact force and contact couple, describing a uniform, hyperelastic, strainlimiting special Cosserat rod. After discussing some attractive features of the constitutive relations (orientation

Rigorous derivation of the Euleralignment model with singular communication weights from a kinetic Fokker–Planckalignment model Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230126
YoungPil Choi, Jeongho KimIn this paper, we present a rigorous derivation of the isothermal Euleralignment model with singular communication weights. We consider a hydrodynamic limit of a kinetic Fokker–Planckalignment model, which is the nonlinear Fokker–Planck equation with the Cucker–Smale alignment force. Our analysis is based on the estimate of relative entropy between macroscopic quantities, together with careful analysis

Smallsignal solutions to a nonlocal crossdiffusion model for interaction of scroungers with rapidly diffusing foragers Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230126
Youshan Tao, Michael WinklerAs a simplified version of a threecomponent taxis cascade model accounting for different migration strategies of two population groups in search of food, a twocomponent nonlocal nutrient taxis system is considered in a twodimensional bounded convex domain with smooth boundary. For any given conveniently regular and biologically meaningful initial data, smallness conditions on the prescribed resource

Ergodicity and longtime behavior of the Random Batch Method for interacting particle systems Math. Models Methods Appl. Sci. (IF 3.5) Pub Date : 20230120
Shi Jin, Lei Li, Xuda Ye, Zhennan ZhouWe study the geometric ergodicity and the longtime behavior of the Random Batch Method for interacting particle systems, which exhibits superior numerical performance in recent largescale scientific computing experiments. We show that for both the interacting particle system (IPS) and the random batch interacting particle system (RB–IPS), the distribution laws converge to their respective invariant